Jennifer Guild holds her bird, Jellybean, at her home in Richmond, Va. Jellybean is Guild’s nippy childhood bird.

Angie Best-Boss has tried changing litter boxes, types of litter, brands of litter. But something has gone terribly wrong with Tiger.

“I loathe my cat,” said the freelance writer in New Palestine, Ind. “Actually, loathe might be too weak of a word. I hate it. The stupid, stupid cat pees. On clothes. Only on clean clothes. And beds. Regardless of what spray I buy, what medicine she takes, she just really, really likes to pee.”

Dogs chewing through table legs. Cats diving for the family dinner. Biting cockatiels. At a time when many people are scrimping on themselves to indulge their animals, the love is lost for owners of infuriating pets.

Still, many can’t bring themselves to dump their wayward animals in shelters. It’s a classic love-hate relationship.

“We all know couples who look like they like to fight. They let fights happen because, it seems, they’re getting something out of it. Some people have that relationship with their pets,” said psychologist Stephanie LaFarge, who specializes in the human-animal bond as senior director of counseling services at the American Society for the Prevention of Cruelty to Animals.

“Some people like to think they love their animals so much they’re willing to be victimized by them,” she said. “It’s proof of how much they love that animal and proof of what a good animal person they are and what a good person they are. It’s part of their identity.”